Trigonometry Examples

$- 7 (12 x + 39) = 23 (3 - 7 x)$

Step 1

Simplify $- 7 (12 x + 39)$ .

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Step 1.1

Rewrite.

$0 + 0 - 7 (12 x + 39) = 23 (3 - 7 x)$

Step 1.2

Simplify by adding zeros.

$- 7 (12 x + 39) = 23 (3 - 7 x)$

Step 1.3

Apply the distributive property.

$- 7 (12 x) - 7 \cdot 39 = 23 (3 - 7 x)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $12$ by $- 7$ .

$- 84 x - 7 \cdot 39 = 23 (3 - 7 x)$

Step 1.4.2

Multiply $- 7$ by $39$ .

$- 84 x - 273 = 23 (3 - 7 x)$

Step 2

Simplify $23 (3 - 7 x)$ .

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Step 2.1

Apply the distributive property.

$- 84 x - 273 = 23 \cdot 3 + 23 (- 7 x)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $23$ by $3$ .

$- 84 x - 273 = 69 + 23 (- 7 x)$

Step 2.2.2

Multiply $- 7$ by $23$ .

$- 84 x - 273 = 69 - 161 x$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Add $161 x$ to both sides of the equation.

$- 84 x - 273 + 161 x = 69$

Step 3.2

Add $- 84 x$ and $161 x$ .

$77 x - 273 = 69$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Add $273$ to both sides of the equation.

$77 x = 69 + 273$

Step 4.2

Add $69$ and $273$ .

$77 x = 342$

Step 5

Divide each term in $77 x = 342$ by $77$ and simplify.

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Step 5.1

Divide each term in $77 x = 342$ by $77$ .

$\frac{77 x}{77} = \frac{342}{77}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $77$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{77 x}{77} = \frac{342}{77}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{342}{77}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{342}{77}$

Decimal Form:

$x = 4.\overline{441558}$

Mixed Number Form:

$x = 4 \frac{34}{77}$